# How did authors ensure that critical points do exist in GAN?

Using an MLP as generator introduces multiple critical points in parameter space. You can read this excerpt from research paper titled Generative Adversarial Nets

In practice, adversarial nets represent a limited family of $$p_g$$ distributions via the function $$G(z; \theta_g)$$, and we optimize $$\theta_g$$ rather than $$p_g$$ itself. Using a multilayer perceptron to define $$G$$ introduces multiple critical points in parameter space. However, the excellent performance of multilayer perceptrons in practice suggests that they are a reasonable model to use despite their lack of theoretical guarantees

The definition of critical point of a function is as follows

We say that $$x=c$$ is a critical point of the function $$f(x)$$ if $$f(c)$$ exists and if either of the following are true. $$f′(c)=0$$ or $$f′(c)$$ doesn't exist

My doubt is: how did the authors ensure that critical points do exist in parameter space? Is it due to some mathematical theorem or by implementation or some other way?